What geometric principal allows us to define trigonometric functions as ratios of sides of triangles and to be confident that they are indeed functions? That is, how do we know that the value of each angle put into a trigonometric function results in exactly one output value

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What geometric principal allows us to define trigonometric functions as ratios of sides of triangles and to be confident that they are indeed functions? That is, how do we know that the value of each angle put into a trigonometric function results in exactly one output value

Trigonometry
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